Embedding Deligne's category $\mathrm{Rep}(S_t)$ in the Heisenberg category

Samuel Nyobe Likeng, Alistair Savage, appendix with Christopher Ryba

Published 2019-05-14Version 1

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category $\mathrm{Rep}(S_t)$, to the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.